ISOMORPHIC SIGNAL ENSEMBLES AND THEIR APPLICATION IN ASYNC-ADDRESS SYSTEMS
The object of consideration is async-address systems using code division of subscribers. The subject of the analysis is quasi-orthogonal ensembles of signals based on code sequences that have normalized characteristics of cross-correlation functions (CCF) and provide reliable separation of subscribers (objects) when exposed to imitation and signal-like interference. The purpose of the analysis is to create a model and methodology for construction a set of the best code sequences ensembles having the ability to quickly change the instance of the set to counter imitation and signal-like interference. The solution is based on algebraic models of code sequences and their CCF representation.
The article proposes a comprehensive technique to construct signal ensembles set having normalized characteristics of the CCF. The quality of the primary ensemble of code sequences is ensured by the procedure for calculating the CCF optimized in the number of look over options. Optimization is based on the basic properties of the Galois field, in particular, on the Galois fields’ isomorphism property. It provides a significant reduction in calculations when choosing the primary ensemble of code sequences with the specified properties of the CCF. The very choice of the best (largest in size) code sequences ensemble relies on the solution of one of the classical combinatorics problems – searching for maximal clique on a graph. The construction of signals ensembles set having normalized characteristics of the CCF is ensured by the use of special combinatorial procedures and algorithms based on the multiplicative properties of Galois fields. An analysis of the effectiveness of known and proven procedures searching for maximal clique is also performed in this article. The work results will be useful in the design of infocommunication systems using complex signals with a large base and variable structure to provide protection from signal structure research and the effects of imitation and signal-like interference
Gold, R. (1968). Maximal recursive sequences with 3-valued recursive cross-correlation functions (Corresp.). IEEE Transactions on Information Theory, 14 (1), 154–156. doi: https://doi.org/10.1109/tit.1968.1054106
Sarwate, D. V., Pursley, M. B. (1980). Crosscorrelation properties of pseudorandom and related sequences. Proceedings of the IEEE, 68 (5), 593–619. doi: https://doi.org/10.1109/proc.1980.11697
Gorgadze, S. F., Boikov, V. V. (2014). Test signals with multilevel subcarriers as applied to satellite radio-navigation systems. Journal of Communications Technology and Electronics, 59 (3), 245–258. doi: https://doi.org/10.1134/s1064226914020028
Gorbenko, I. D., Zamula, А. А., Semenko, A. E., Morozov, V. L. (2017). Method for complex improvement of characteristics of orthogonal ensembles based on multiplicative combining of signals of different classes. Telecommunications and Radio Engineering, 76 (18), 1581–1594. doi: https://doi.org/10.1615/telecomradeng.v76.i18.10
Golomb, S. W., Gong, G. (2005). Signal Design for Good Correlation. Cambridge University Press. doi: https://doi.org/10.1017/cbo9780511546907
Stasev, Y., Kuznetsov, A., Karpenko, O., Sai, V. (2012). Discrete signals with multi-level correlation function. Telecommunications and Radio Engineering, 71 (1), 91–98. doi: https://doi.org/10.1615/telecomradeng.v71.i1.100
Mazepa, R. B., Mikhaylov, V. Y. (2017). Performance characteristics of the isomorphic ensemble of signals for async-address systems. 2017 Systems of Signal Synchronization, Generating and Processing in Telecommunications (SINKHROINFO). doi: https://doi.org/10.1109/sinkhroinfo.2017.7997539
Vladimirov, S., Kognovitsky, O. (2019). Dual Basis Based Processing of Wideband Gordon–Mills–Welch Sequences Based on Two Linear Registers. Proceedings of Telecommunication Universities, 5 (2), 49–58. doi: https://doi.org/10.31854/1813-324x-2019-5-2-49-58
Orel, D., Zhuk, A., Zhuk, E., Luganskaia, L. (2017). A method of forming code sets for CDMA in communication, navigation and control systems. CEUR Workshop Proceedings, 1837, 158–167.
Sultanov, B. V., Rumyantseva, N. B., Zefirov, S. L. (2013). Analysis of the fast acquisition method in frequency hopping systems. Journal of Communications Technology and Electronics, 58 (6), 526–534. doi: https://doi.org/10.1134/s1064226913050094
Kuzovnikov, A. V. (2014). Study of the methods for developing jamming-immune communications systems with the use of wavelet-modulated signals. Journal of Communications Technology and Electronics, 59 (1), 61–70. doi: https://doi.org/10.1134/s1064226914010069
Viterbi, A. J. (1966). Principles of coherent communication. McGraw-Hill, 321.
Monakhova, E. A. (2011). Structural and communicative properties of circulant networks. Prikladnaya Diskretnaya Matematika, 13, 92–115. doi: https://doi.org/10.17223/20710410/13/8
Hou, B., Wang, Z., Chen, Q., Suo, B., Fang, C., Li, Z., Ives, Z. G. (2016). Efficient Maximal Clique Enumeration Over Graph Data. Data Science and Engineering, 1 (4), 219–230. doi: https://doi.org/10.1007/s41019-017-0033-5
Utkina, I. (2018). Using Modular Decomposition Technique to Solve the Maximum Clique Problem. Springer Proceedings in Mathematics & Statistics, 121–131. doi: https://doi.org/10.1007/978-3-319-96247-4_8
Wildman, J. (2020). Bron-Kerbosch maximal clique finding algorithm. MATLAB Central File Exchange. Available at: https://www.mathworks.com/matlabcentral/fileexchange/30413-bron-kerbosch-maximal-clique-finding-algorithm
Dharwadker, A. The Clique Algorithm. Available at: http://www.dharwadker.org/clique/
MaxCliquePara. Available at: http://commsys.ijs.si/~matjaz/maxclique/MaxCliquePara/
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